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Photonic Crystals:
Molding the Flow of Light
John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn & Robert D. Meade

Book Description | Reviews
Chapter 1 [in PDF format]


Preface to the Second Edition xiii
Preface to the First Edition xv

Chapter 1: Introduction 1
Controlling the Properties of Materials 1
Photonic Crystals 2
An Overview of the Text 3

Chapter 2: Electromagnetism in Mixed Dielectric Media 6
The Macroscopic Maxwell Equations 6
Electromagnetism as an Eigenvalue Problem 10
General Properties of the Harmonic Modes 12
Electromagnetic Energy and the Variational Principle 14
Magnetic vs. Electric Fields 16
The Effect of Small Perturbations 17
Scaling Properties of the Maxwell Equations 20
Discrete vs. Continuous Frequency Ranges 21
Electrodynamics and Quantum Mechanics Compared 22
Further Reading 24

Chapter 3: Symmetries and Solid-State Electromagnetism 25
Using Symmetries to Classify Electromagnetic Modes 25
Continuous Translational Symmetry 27
Index guiding 30
Discrete Translational Symmetry 32
Photonic Band Structures 35
Rotational Symmetry and the Irreducible Brillouin Zone 36
Mirror Symmetry and the Separation of Modes 37
Time-Reversal Invariance 39
Bloch-Wave Propagation Velocity 40
Electrodynamics vs. Quantum Mechanics Again 42
Further Reading 43

Chapter 4: The Multilayer Film: A One-Dimensional Photonic Crystal 44
The Multilayer Film 44
The Physical Origin of Photonic Band Gaps 46
The Size of the Band Gap 49
Evanescent Modes in Photonic Band Gaps 52
Off-Axis Propagation 54
Localized Modes at Defects 58
Surface States 60
Omnidirectional Multilayer Mirrrors 61
Further Reading 65

Chapter 5: Two-Dimensional Photonic Crystals 66
Two-Dimensional Bloch States 66
A Square Lattice of Dielectric Columns 68
A Square Lattice of Dielectric Veins 72
A Complete Band Gap for All Polarizations 74
Out-of-Plane Propagation 75
Localization of Light by Point Defects 78
Point defects in a larger gap 83
Linear Defects and Waveguides 86
Surface States 89
Further Reading 92

Chapter 6: Three-Dimensional Photonic Crystals 94
Three-Dimensional Lattices 94
Crystals with Complete Band Gaps 96
Spheres in a diamond lattice 97
Yablonovite 99
The woodpile crystal 100
Inverse opals 103
A stack of two-dimensional crystals 105
Localization at a Point Defect 109
Experimental defect modes in Yablonovite 113
Localization at a Linear Defect 114
Localization at the Surface 116
Further Reading 121

Chapter 7: Periodic Dielectric Waveguides 122
Overview 122
A Two-Dimensional Model 123
Periodic Dielectric Waveguides in Three Dimensions 127
Symmetry and Polarization 127
Point Defects in Periodic Dielectric Waveguides 130
Quality Factors of Lossy Cavities 131
Further Reading 134

Chapter 8: Photonic-Crystal Slabs 135
Rod and Hole Slabs 135
Polarization and Slab Thickness 137
Linear Defects in Slabs 139
Reduced-radius rods 139
Removed holes 142
Substrates, dispersion, and loss 144
Point Defects in Slabs 147
Mechanisms for High Q with Incomplete Gaps 149
Delocalization 149
Cancellation 151
Further Reading 155

Chapter 9: Photonic-Crystal Fibers 156
Mechanisms of Confinement 156
Index-Guiding Photonic-Crystal Fibers 158
Endlessly single-mode fibers 161
The scalar limit and LP modes 163
Enhancement of nonlinear effects 166
Band-Gap Guidance in Holey Fibers 169
Origin of the band gap in holey fibres 169
Guided modes in a hollow core 172
Bragg Fibers 175
Analysis of cylindrical fibers 176
Band gaps of Bragg fibers 178
Guided modes of Bragg fibers 180
Losses in Hollow-Core Fibers 182
Cladding losses 183
Inter-modal coupling 187
Further Reading 189

Chapter 10: Designing Photonic Crystals for Applications 190
Overview 190
A Mirror, a Waveguide, and a Cavity 191
Designing a mirror 191
Designing a waveguide 193
Designing a cavity 195
A Narrow-Band Filter 196
Temporal Coupled-Mode Theory 198
The temporal coupled-mode equations 199
The filter transmission 202
A Waveguide Bend 203
A Waveguide Splitter 206
A Three-Dimensional Filter with Losses 208
Resonant Absorption and Radiation 212
Nonlinear Filters and Bistability 214
Some Other Possibilities 218
Reflection, Refraction, and Diffraction 221
Reflection 222
Refraction and isofrequency diagrams 223
Unusual refraction and diffraction effects 225
Further Reading 228

Epilogue 228
A Comparisons with Quantum Mechanics 229
B The Reciprocal Lattice and the Brillouin Zone 233
The Reciprocal Lattice 233
Constructing the Reciprocal Lattice Vectors 234
The Brillouin Zone 235
Two-Dimensional Lattices 236
Three-Dimensional Lattices 238
Miller Indices 239
C Atlas of Band Gaps 242
A Guided Tour of Two-Dimensional Gaps 243
Three-Dimensional Gaps 251
D Computational Photonics 252
Generalities 253
Frequency-Domain Eigenproblems 255
Frequency-Domain Responses 258
Time-Domain Simulations 259
A Planewave Eigensolver 261
Further Reading and Free Software 263

Bibliography 265
Index 283

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File created: 4/21/2017

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